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A Further Study on Asymptotic Functions via Variational Analysis

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Abstract

We use variational analysis for studying asymptotic (recession or horizon) functions. We introduce the upper and lower asymptotic operators and study their domain and image. Moreover, we characterize their fixed points and zeros. Finally, we establish continuity properties of this operator, i.e., the convergence of asymptotic functions of convergent sequences of functions.

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Acknowledgements

The authors want to express their gratitude to the referees for their criticism and suggestions that helped to improve the paper. This research was partially supported by Conicyt-Chile throughout Projects Fondecyt Iniciación 11180320 (Lara) and Fondecyt Regular 1181368 (López), by Universidad de Tarapacá throughout project UTA-Mayor 4739-18 (López) and by Conselho Nacional de Desenvolvimento Científico e Tecnológico Grant 306247/2015-1 and Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro Grant Cientistas de Nosso Estado E-26/201.584/2014 (Svaiter).

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Authors and Affiliations

  1. Departamento de Matemática, Universidad de Tarapacá, Arica, Chile

    Felipe Lara & Rubén López

  2. Instituto Nacional de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, Brazil

    Benar F. Svaiter

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  1. Felipe Lara
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  2. Rubén López
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  3. Benar F. Svaiter
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Correspondence to Felipe Lara.

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Lara, F., López, R. & Svaiter, B.F. A Further Study on Asymptotic Functions via Variational Analysis. J Optim Theory Appl 182, 366–382 (2019). https://doi.org/10.1007/s10957-019-01507-w

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  • DOI: https://doi.org/10.1007/s10957-019-01507-w

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